Comparing the performance potential of speckle contrast optical spectroscopy and diffuse correlation spectroscopy for cerebral blood flow monitoring using Monte Carlo simulations in realistic head geometries

Abstract. Significance The non-invasive measurement of cerebral blood flow based on diffuse optical techniques has seen increased interest as a research tool for cerebral perfusion monitoring in critical care and functional brain imaging. Diffuse correlation spectroscopy (DCS) and speckle contrast optical spectroscopy (SCOS) are two such techniques that measure complementary aspects of the fluctuating intensity signal, with DCS quantifying the temporal fluctuations of the signal and SCOS quantifying the spatial blurring of a speckle pattern. With the increasing interest in the use of these techniques, a thorough comparison would inform new adopters of the benefits of each technique. Aim We systematically evaluate the performance of DCS and SCOS for the measurement of cerebral blood flow. Approach Monte Carlo simulations of dynamic light scattering in an MRI-derived head model were performed. For both DCS and SCOS, estimates of sensitivity to cerebral blood flow changes, coefficient of variation of the measured blood flow, and the contrast-to-noise ratio of the measurement to the cerebral perfusion signal were calculated. By varying complementary aspects of data collection between the two methods, we investigated the performance benefits of different measurement strategies, including altering the number of modes per optical detector, the integration time/fitting time of the speckle measurement, and the laser source delivery strategy. Results Through comparison across these metrics with simulated detectors having realistic noise properties, we determine several guiding principles for the optimization of these techniques and report the performance comparison between the two over a range of measurement properties and tissue geometries. We find that SCOS outperforms DCS in terms of contrast-to-noise ratio for the cerebral blood flow signal in the ideal case simulated here but note that SCOS requires careful experimental calibrations to ensure accurate measurements of cerebral blood flow. Conclusion We provide design principles by which to evaluate the development of DCS and SCOS systems for their use in the measurement of cerebral blood flow.


S1. Example of typical dark noise for silicon CMOS camera
Because a large range of exposure times are explored in this work (1 μs to 100 ms), the assumption for the model neglecting the contributions of dark noise may be violated.To explore this experimentally, we collected dark frames using a silicon CMOS camera (Basler ace acA1300-200um) at a range of exposure times and computed the average intensity collected as well as the combination of dark and read noise variance.Average intensity and variance are computed on windows of size 8 pixels by 8 pixels with 0% overlap, and the average and variance values for each window are averaged across multiple collected dark images (20 images per exposure time).found to elevate at exposure times >~25 ms.While this effect would be noticeable for the longer exposures and would result in an increased coefficient of variation, for the simulations performed with the described camera settings, CoV estimates for exposure times >6.67 ms already increase due to the loss of frame averaging.Additionally, in practice, the average dark frame and dark variance at the long exposure would be subtracted, accounted for the longer exposure.The optimal CNR operating point for most measurements presented occurs at an exposure time shorter than 25 ms, and although the assumption does break down for the longer exposure range, it should not have a large effect on the selection of optimal operating parameters.are not observed until exposure times >~25ms.These results would indicate for a reasonably similar camera, measurements with exposure times less than ~25ms will be relatively unaffected by the influence of dark current, and the assumption is reasonably valid for the vast majority of optimal operating parameters explored in the main text.

S2. Sensitivity to changes in cerebral blood flow (CBF) as a function of the relative change in CBF.
In this work, a cerebral blood flow perturbation of 20% was selected to evaluate the cerebral sensitivity of the SCOS and DCS measurements.This CBF change is consistent with changes we have observed in previous studies in response to both functional activation and physiological manipulations 14,31 .While it is generally assumed that sensitivity to the cerebral signal is relatively constant within the physiologic range of blood flow values, we investigate the effect of changing the magnitude of the CBF perturbation on the extracted BFi and the sensitivity of the measurement.
In Figure S2   (d.).While there are differences across the perturbation magnitude range, the findings here would not appreciably affect the results presented in the main text.

S3. Expanded description of the regimes present in the SCOS contrast-to-noise curves at different exposure times:
For the different laser illumination strategies explored, the shape of the SCOS contrast-to-noise curve is relatively complicated, and the shapes reveal the interplay between the exposure time, max frame rate, maximum laser power available, the ANSI limited source power, and the noise properties of the camera.In Figure 5 in the main text, we explored four laser illumination strategies: 1) single CW source, 2) multiple CW sources to utilize the entire max laser power without breaking the ANSI limit, 3) a pulse width modulated strategy where the source input power (Pin) is modulated such that the product of the input power, exposure time (Texp), and the frame rate of the camera (fs) is less than or equal to the ANSI limited power (PANSI) for a 3.5 mm diameter, single-source position, expressed as   *   *   ≤   , and 4) a pulse width modulated strategy where the frame rate of the camera is modulated such that the product of the maximal input power (Pmax), exposure time and the frame rate of the camera is less than or equal to the provides optimal performance.The boundary between the region labeled (2) and the region labeled (3) occurs at the exposure time equal to the inverse of the max frame rate and represents the point at which camera frame rate and the degree of frame averaging will be reduced by the increased exposure time.For most measurement conditions, a monotonic decrease in CNR is seen for all source configurations after this exposure time, though there are cases, as seen in Figure 7.b (s/p ratio = 2.0), where the peak of the CNR curve is reached after the frame rate is limited by the exposure time.This difference represents a condition in which the measurement is not shot noise limited and the increase in the number of collected photons outweighs the reduction in frame averaging.
Figure S3.Expanded description of the factors that differentiate the different laser pulsing strategies as well as describe the different regimes of the SCOS CNR curve.In (a.) the input power used for each strategy is detailed.Both pulsed source implementations match the multi-source CW input power until the boundary between regions ( 1) and ( 2), after which the max power limiting strategy approaches the single CW source approach.In (b.) the frame rate used for each strategy is detailed.The reduction in frame rate from the frame rate limiting strategy can be seen after the boundary between regions ( 1) and ( 2), and the monotonic decrease continues with increasing exposure time to maintain a duty cycle equal to the ratio of the ANSI-limited single source power and the max power of the laser, as seen in (c.).For the other laser strategies, the duty cycle monotonically increases until reaching region (3), when the exposure time limits the frame rate of the measurement, and the duty cycle reaches 100%.The results presented in  For each source-detector separation at each probe position, the partial pathlength in each tissue type and the dimensionless momentum transfer accrued over detected photon trajectories is saved (1).Additionally, the profile of diffuse reflectance at each probe position is computed to scale the expected photon flux at each detector.Using the Monte Carlo outputs, electric field autocorrelation functions ( 1 ()) are computed (2).
The photon flux per fiber mode per second is estimated using the illumination strategy and the scaled diffuse reflectance curve (3).For DCS and SCOS, the appropriate model for scaling the per mode photon flux is applied to calculate the per detector photon flux, and the appropriate model for the coherence parameter is used to calculate a technique specific β value (4).For each method, the appropriate signal and noise model is applied, and multiple instances of noisy data for each investigated condition are generated (5).Finally, the noisy data are fit for the blood flow index using the solution to the correlation diffusion equation for a semi-infinite media in the reflectance geometry and the appropriate fitting model.In the case of DCS, the Siegert relation is used, and in the case of SCOS, inversion of the speckle contrast integral is used (6).
Figure S1, the average intensity (Figure.S1.a) and combined noise variance (Figure S1.b) distributions are relatively flat for much of the exposure time range and are only

Figure S1 .
Figure S1.Comparison of the dark intensity (a.) and the dark variance (b.) measured as a function of exposure time on a representative silicon CMOS camera.For both average intensity and variance, increases in the parameter valuesare not observed until exposure times >~25ms.These results would indicate for a reasonably similar camera, measurements with exposure times less than ~25ms will be relatively unaffected by the influence of dark current, and the assumption is reasonably valid for the vast majority of optimal operating parameters explored in the main text.
, the comparison of absolute cerebral sensitivity (Fig. S2.a and S2.c) and difference in cerebral sensitivity relative to the cerebral sensitivity computed for a 10% change in CBF (Fig S2.b and S2.d) are shown for both DCS and SCOS for a range of CBF changes from 10% to 100%.From the results, cerebral sensitivity of DCS is less affected by the change in magnitude of the perturbation as compared to the cerebral sensitivity of SCOS, though the sensitivities found have a relatively small range across the range of changes in CBF.These results may also suggest shortcomings of the semi-infinite model applied to multi-layered tissue, as previous studies using multi-layered models have demonstrated accurate recovery of relative changes in CBF 33 .

Figure S2 .
Figure S2.Comparison of the estimated cerebral sensitivity for both DCS (a.) and SCOS (c.).The change in estimated cerebral sensitivity as a function of perturbation magnitude is also shown for both DCS (b.) and SCOS ANSI limited power for a 3.5 mm diameter, single-source position, expressed as   *   *   ≤   .These figures reveal three operation regimes for SCOS, which affect each of the different illumination styles in different ways.Shown in FigureS3, we expand upon the figures shown in the main text and detail the input power used for each strategy at a given exposure time (Figure S3.a), the frame rate utilized for each exposure time (Figure S3.b), the duty cycle of the measurement (Figure S3.c), and a figure depicting the data shown in Figure 5.b with shading to demarcate the transition from one regime of operation to another.In the region labeled (1) in Figure S3.d, the simulated measurement has yet to reach the point of being ANSI limited for the pulsed configurations.In this region the CNR for all source delivery strategies exhibits a monotonic increase with exposure time, indicating the measurements are not yet shot noise limited.At the boundary of the region labeled (1) and the region labeled (2), the power delivery for the pulsed laser strategies reaches the ANSI limit, given by   *   *   =   , and marks the first point of divergence between the different implementations.The selection of either reducing the input power (Figure S3.a) or reducing the frame rate (Figure S3.b) results in a different shape in the CNR curve.As was noted in the main text, for long separation measurements, increasing the instantaneous photon flux during the exposure time is more beneficial for the measurement CNR, as seen in Figure S3.d.Further, for measurements made with sufficiently small s/p ratio to reach shot noise limited performance, for the simulations performed in this work of the pulsed laser strategies, the exposure time equal to     * Figure S3.Expanded description of the factors that differentiate the different laser pulsing strategies as well as describe the different regimes of the SCOS CNR curve.In (a.) the input power used for each strategy is detailed.Both pulsed source implementations match the multi-source CW input power until the boundary between regions (1) and (2), after which the max power limiting strategy approaches the single CW source approach.In (b.) the frame rate used for each strategy is detailed.The reduction in frame rate from the frame rate limiting strategy can be seen after the boundary between regions (1) and (2), and the monotonic decrease continues with increasing exposure time to maintain a duty cycle equal to the ratio of the ANSI-limited single source power and the max power of the laser, as seen in (c.).For the other laser strategies, the duty cycle monotonically increases until reaching region (3), when the exposure time limits the frame rate of the measurement, and the duty cycle reaches 100%.The results presented in Figure 5.b are presented again in (d.) with additional labeling describing the transitions between different regions of the curve.The boundary between regions (1) and (2) occurs at an exposure time equal to     *   , and the

Figure S4 .
Figure S4.Visual depiction of the simulation steps required to convert the outputs of the Monte Carlo simulations into estimates of blood flow index.Each step depicted in the figure is performed for each of the probe positions explored in this work.For each source-detector separation at each probe position, the partial pathlength in each tissue type and the dimensionless momentum transfer accrued over detected photon trajectories is saved (1).Additionally, the profile of diffuse reflectance at each probe position is computed to scale the expected photon flux at each detector.Using the Monte Carlo outputs, electric field autocorrelation functions ( 1 ()) are computed (2).The photon flux per fiber mode per second is estimated using the illumination strategy and the scaled diffuse reflectance curve (3).For DCS and SCOS, the appropriate model for scaling the per mode photon flux is applied to calculate the per detector photon flux, and the appropriate model for the coherence parameter is used to calculate a technique specific β value (4).For each method, the appropriate signal and noise model is applied, and multiple instances of noisy data for each investigated condition are generated (5).Finally, the noisy data are fit for the blood flow index using the solution to the correlation diffusion equation for a semi-infinite media in the reflectance geometry and the appropriate fitting model.In the case of DCS, the Siegert relation is used, and in the case of SCOS, inversion of the speckle contrast integral is used (6).